The MILES star HD39970 is significantly reddened by interstellar extinction so does not look like the standard Pickles spectrum. See the attached MILES library spectra (Dark blue is the observed spectrum, uncorrected. Light blue is how the spectrum would look without interstellar extinction.) Did you use the uncorrected MILES spectrum or the Pickles spectrum to calculate the instrument response?

Hi Robinso I de-reded the profile of the base Miles with the coefficient 0.82I recorded it in "mybase", and used the result for the instrumental answerthe profile of the Be is a little differentthank you for these valuable indications question: can we do the same with pickles?have a good day

You should not deredden the MILES spectrum in ISIS. The MILES spectra in ISIS are the original spectra as measured (including interstellar reddening) These are the correct spectra to use to calculate the instrument response.

If you use your calculated instrument response with your measurement of the MILES star it should match the MILES spectrum in ISIS exactly (not the standard Pickles spectrum.)

You could try reddening the Pickles spectrum but this will only be approximately correct as the exact effect of reddening is unknown and the actual MILES star might no be exactly like the Pickles standard.